Depending on how much mystery you want behind exactly what is the root cause for these undead, here are some ideas to consider:
A) A powerful demon is behind it all, but no one knows that. A secretive cult that worships this demon has performed (or may even still be performing) a ritual to awaken all the dead within a large radius. Now these undead are spilling out of this area and the party encounters them on the outskirts. Plot progress could involve several waves of undead, rescuing villagers along the way and ultimately learning of the secret cult. Eventually, the party uncovers various agents of the cult, then tracks them back to their main hidden temple for a showdown to end the undead plague. But before they are totally successful, they draw the attention and wrath of the demon. The demon may be extremely hard to defeat, but could have an achilles heel that they learn of to help defeat him. The party level can vary wildly here. For low-level parties, the walking dead may just be skeletons and zombies, while somewhat higher level parties square off against ghouls, ghasts and so forth. Still higher level groups may be facing vampires, wraiths and so forth.
B) An experiment of a high level necromancer has gone awry. A new spell or ritual being researched has had unintended side effects and unleashed a horde of undead upon the land. The effect of the spell is such that all creatures killed, raise up from the dead within 24 hours intent on killing all living creatures they find. Party as well as everyone else is baffled by the undead and try to fight them only to find them reanimating again the next day. Divination magic or some other clues may be able to help reveal the source of the undead plague or a method to halt it. Reaching the necromancer's abode will involve a nasty battle thru even more waves of undead, magical traps and perhaps having to square off against the necromancer himself. He may not view his experiment as a failure...
C) A rift to the negative energy plane has formed (accidental, magical, etc), and now all creatures near it are being drained and turned into undead. The rift may be expanding or perhaps a new form of undead has developed which is quickly spreading almost like a disease. The party can once again battle waves of undead, and eventually learn of the rift. Then they must find a way to close the rift, likely requiring some magical means. It's possible that getting close to the rift may even cause negative levels to be applied to the party as it sucks their very lifeforces as well.
Once you have a basic root cause of the undead determined, you can determine where this has happened and what impact it has had. In remote areas there will be less undead (fewer bodies to reanimate, etc), but also the people could be more ignorant of the problem, etc. The party may be the only people nearby who can help. On the other hand, if this happens in or near a large population center there could be many undead and people will quickly become aware of the problem. But there are also likely to be many other adventurers as well as priests to help battle the undead in such a populated area. IMHO, a smaller village, perhaps one with only a druid as their main spiritual healer would be an ideal spot for undead to attack, yet allow the party to turn the tide. By the time the party arrives to help, perhaps 3/4's of the town has been killed and turned into undead and the few survivors are fighting a losing battle holed up inside an Inn.
To keep the fights from getting overly repetitious, I suggest mixing up the undead and tossing in things like animal skeletons or animal zombies just to show that the undead are a threat to everything in their path, not just humanoids.
